Ovalization restraint in four-point bending tests of tubes

Four-point bending tests have been a staple in many structural engineering experiments as a reliable way of assessing the bending resistance of circular hollow sections, tubes and cylindrical shells, and they continue to be widely performed. However, relatively little attention appears to have been paid to quantify the effects of different boundary conditions on the test outcome. In particular, the restraint or freedom given to the cross-section at the ends of the specimen to ovalize can have a significant impact when the specimen is in an appropriate length range. Ovalization is an elastic geometrically nonlinear phenomenon that is known to reduce the elastic bending resistance by as much as half in long tubes or cylinders. This paper presents a short distillation of some recent advances in understanding the buckling of cylindrical shells under uniform bending, identifying the strong influence of the cylinder length on cross-section ovalization. A sample set of three-dimensional load application arrangements used in existing four-point bending tests was simulated using finite elements, allowing an assessment of the differences caused by pre-buckling ovalization and its effect on the tested bending resistance. The study is limited to elastic behaviour to identify the effect of ovalization alone in reducing the stiffness without material nonlinearity. The outcomes demonstrate that maintaining circularity at the inner load application points by appropriate stiffening has a significant effect. With freedom to ovalize, a significant reduction in stiffness occurs, leading to much lower bending resistance at buckling than may be achievable in practical applications